The prime factorization of 65 is 5 and 13. To find this, we need to break down the number 65 into its prime factors.
First, we can determine if 65 is divisible by the smallest prime number, which is 2. Since 65 is odd, it is not divisible by 2. Next, we check for divisibility by 3. Adding the digits of 65 (6 + 5), we get 11, which is not divisible by 3, so 65 isn’t either.
Now, we check 5, which does divide evenly into 65 (since it ends in a 5). We find that:
- 65 ÷ 5 = 13
At this point, we’ve factored 65 into 5 and 13. Next, we confirm that both 5 and 13 are prime numbers, meaning they cannot be divided by any other numbers besides 1 and themselves. Therefore, the complete prime factorization of 65 is:
- 5 × 13